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Chapter 6: Problem 57

The average birth weight of domestic cats is about 3 ounces. Assume that the distribution of birth weights is Normal with a standard deviation of \(0.4\) ounce. a. Find the birth weight of cats at the 90 th percentile. b. Find the birth weight of cats at the 10 th percentile.

Short Answer

Expert verified
The weight of cats at the 90th percentile is approximately 3.512 ounces, and at the 10th percentile is approximately 2.488 ounces.

Step by step solution

01

Determine the Z-score for the 90th percentile

The 90th percentile corresponds to a z-score of 1.28. This is found from the Z-table or using statistical software. A Z-score is how many standard deviations away from the mean a certain value is.
02

Compute the 90th percentile

A z-score is calculated using the formula Z = (X - 渭)/蟽 where X is the value, 渭 is the mean and 蟽 is the standard deviation. Solving for X gives X = Z蟽 + 渭. Substituting in the z-score for the 90th percentile (1.28), the mean (3 ounces) and the standard deviation (0.4 ounces) gives X = 1.28(0.4) + 3 = 3.512 ounces.
03

Find the Z-score for the 10th percentile

The 10th percentile corresponds to a Z-score -1.28. Again, this can be found from the Z-table or using statistical software.
04

Compute the 10th percentile

Using the formula X = Z蟽 + 渭, and the Z-score for the 10th percentile (-1.28), the mean (3 ounces) and the standard deviation (0.4 ounces), gives X = -1.28(0.4) + 3 = 2.488 ounces.

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